We also consider extraneous counts due to detector dark counts or from stray-light where \(p_{ec}\)  is the probability per pulse. Another source of errors is due to errors in the polarization states or their measurement and we characterise these by the intrinsic quantum bit error rate or \(QBER_I\)  that is independent of channel loss. We also account for detector after-pulsing where we assume the value \(p_{ap}=10^{-3}\) , consistent with values used in previous modelling of fibre and free-space QKD systems [1]}, [2]}. For convenience, fixed modelling parameter are listed in table REF .
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